Model predictive control of nonlinear stochastic partial differential equations with application to a sputtering process

Abstract

A method is developed for model predictive control of nonlinear stochastic partial differential equations (PDEs) to regulate the state variance, which physically represents the roughness of a surface in a thin film growth process, to a desired level. Initially a nonlinear stochastic PDE is formulated into a system of infinite nonlinear stochastic ordinary differential equations by using Galerkin's method. A finite-dimensional approximation is then derived that captures the dominant mode contribution to the state variance. A model predictive control problem is formulated, based on the finite-dimensional approximation, so that the future state variance can be predicted in a computationally efficient way. To demonstrate the method, the model predictive controller is applied to the stochastic Kuramoto-Sivashinsky equation, and the kinetic Monte Carlo model of a sputtering process to regulate the surface roughness at a desired level. © 2008 American Institute of Chemical Engineers AIChE J, 2008